In this paper, we aim to provide a comprehensive view of the unemployment dynamics generated by different structural shocks. We show that the relative contribution of the job finding and separation rates to the unemployment dynamics depends on a type of structural shocks. Identified using a sign restrictions approach, the shocks of our Bayesian Structural VAR model capture the possible shifts in the three conditions determining labor market equilibrium in any matching models, namely: the Beveridge curve, the job creation condition, and the job destruction condition. Using US data we then identify a shock to the profitability of a match (the aggregate shock), a shock specific to the existing jobs (job-specific shock) and a shock to the efficiency of the matching process (search shock). The two former shocks generate a quite balanced contribution of the two transition rates to the volatility of unemployment, whereas the search shock implies a disproportionate importance of the job finding rate. We find the same result for French data, which assesses the robustness of the pattern generated by these structural shocks. The difference between the two countries lies more in the relative importance of the shocks. The search shock appears more significant in France, which in the end reinforces the predominant role of the job finding rate in this country.